# CLEAN WORKSPACE AND LOAD PACKAGES --------------------------------------------
rm(list = ls())
library(datasim)
library(tidyverse)
## ── Attaching packages ────────────────────────────────── tidyverse 1.2.1 ──
## ✔ ggplot2 2.2.1.9000 ✔ purrr 0.2.4
## ✔ tibble 1.4.2 ✔ dplyr 0.7.4
## ✔ tidyr 0.8.0 ✔ stringr 1.3.0
## ✔ readr 1.1.1 ✔ forcats 0.3.0
## ── Conflicts ───────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ dplyr::vars() masks ggplot2::vars()
# SIMULATE MULTIVARIATE SPATIAL DATA -------------------------------------------
# set.seed(4)
Corr <- matrix(c(1, -0.3, 0, -0.3, 1, 0.3, 0, 0.3, 1), nrow = 3)
sigmas <- rep(0.4^0.5, 3)
D <- diag(sigmas)
Cov <- D %*% Corr %*% D
# beta <- c(-0.5, 0, 0.5)
beta <- c(0, 0, 0)
variance <- 0.6 * matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1), nrow = 3)
cor.model <- "exp_cor"
cor.params <- list(list(phi = 0.04), list(phi = 0.04), list(phi = 0.1))
f <- list(
mean ~ mfe(x1, beta = get("beta")) +
mre(factor(id), sigma = get("Cov")) +
mgp(list(s1), variance = get("variance"), cor.model = get("cor.model"),
cor.params = get("cor.params")),
sd ~ I(0)
)
n <- 300
m <- 3
(data_geo <- sim_model(formula = f, n = n, responses = m))
## # A tibble: 900 x 9
## id x1 s1 mre.factor.mean mgp.list.mean mean sd
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0.476 0.285 -0.185 0.904 0.719 0.
## 2 2 -0.856 0.729 -0.0733 -1.13 -1.20 0.
## 3 3 -1.84 0.0912 0.477 -0.354 0.123 0.
## 4 4 0.191 0.527 0.0108 1.18 1.19 0.
## 5 5 0.0108 0.240 0.329 -0.208 0.121 0.
## 6 6 -1.58 0.379 -0.251 0.252 0.00173 0.
## 7 7 -0.675 0.690 -0.0572 0.280 0.223 0.
## 8 8 1.07 0.621 -0.253 -0.977 -1.23 0.
## 9 9 0.483 0.811 0.000684 -0.276 -0.275 0.
## 10 10 1.11 0.682 -0.594 0.503 -0.0912 0.
## # ... with 890 more rows, and 2 more variables: response <dbl>,
## # response_label <int>
# knitr::kable(head(data_model, 10))
X <- matrix(rnorm(20), 10, 2)
# VISUALIZE MULTIVARIATE SPATIAL DATA ------------------------------------------
ggplot(data_geo, aes(x1, response)) +
geom_smooth(aes(col = factor(response_label))) +
geom_point(aes(col = factor(response_label)))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
ggplot(data_geo, aes(s1, mgp.list.mean)) +
geom_line(aes(col = factor(response_label)))
data_geo %>%
dplyr::select(id, mre.factor.mean, response_label) %>%
spread(response_label, mre.factor.mean) %>%
dplyr::select(-id) %>%
GGally::ggpairs(aes(fill = "any"))
data_geo_wide <- data_geo %>%
dplyr::rename(ability = response, id_person = id) %>%
gather(var, value, mre.factor.mean:ability) %>%
mutate(var = paste0(var, response_label)) %>%
select(-response_label) %>%
spread(var, value)
# SIMULATE ITEM FACTOR DATA ----------------------------------------------------
q <- 10
init_data <- purrr::map(1:q, ~ data_geo_wide) %>%
purrr::reduce(rbind)
# n <- 300
difficulty <- matrix((1:q - 5)/10 * 2, nrow = 1)
discrimination1 <- seq(0.4, 1.5, length.out = q)
discrimination2 <- runif(q, 0, 2)
discrimination3 <- runif(q, 0, 2)
discrimination1[1] <- 1
discrimination1[c(3, 5, 8)] <- 0
discrimination2[1:2] <- c(0, 1)
discrimination2[c(4, 5, 10)] <- 0
# discrimination3[1:3] <- c(0, 0, 1)
# discrimination1 <- discrimination1 * 0.3
# discrimination2 <- discrimination2 * 0.3
cbind(discrimination1, discrimination2, discrimination3)
## discrimination1 discrimination2 discrimination3
## [1,] 1.0000000 0.00000000 0.03342079
## [2,] 0.5222222 1.00000000 1.93959064
## [3,] 0.0000000 1.80589290 1.54502217
## [4,] 0.7666667 0.00000000 1.58316375
## [5,] 0.0000000 0.00000000 0.13343296
## [6,] 1.0111111 1.99441057 1.51071104
## [7,] 1.1333333 0.77046483 1.04485630
## [8,] 0.0000000 0.01718154 0.12162534
## [9,] 1.3777778 0.86570335 1.98672634
## [10,] 1.5000000 0.00000000 0.80690463
f <- list(
prob ~ mfa(ones, beta = get("difficulty")) +
mfe(ability1, beta = get("discrimination1")) +
mfe(ability2, beta = get("discrimination2")),
# + mfe(ability3, beta = get("discrimination3")),
size ~ I(1)
)
data_long <- sim_model(formula = f,
link_inv = list(pnorm, identity),
generator = rbinom,
responses = q,
n = n,
init_data = init_data
)
data_long <- dplyr::rename(data_long, subject = id,
item = response_label, y = response)
# VISUALIZE ITEM FACTOR DATA ---------------------------------------------------
explor <- data_long %>%
group_by(subject) %>%
summarize(endorse = mean(y),
ability1 = unique(ability1),
ability2 = unique(ability2),
# ability3 = unique(ability3),
x1 = unique(x1))
ggplot(explor, aes(ability1, endorse)) + geom_point(alpha = 0.5)
ggplot(explor, aes(ability2, endorse)) + geom_point(alpha = 0.5)
# ggplot(explor, aes(ability3, endorse)) + geom_point(alpha = 0.5)
# ggplot(explor, aes(x1, endorse)) + geom_point(alpha = 0.5)
# PREPARE DATA -----------------------------------------------------------------
response <- data_long$y
dist <- as.matrix(dist(dplyr::select(data_geo_wide, s1)))
# dist <- as.matrix(dist(dplyr::select(data_geo_wide, s1)[order(data_geo_wide$s1),]))
# dist <- dist[order(data_geo_wide$s1),]
n
## [1] 300
q
## [1] 10
m <- 2
# iter <- 5 * 10 ^ 4
iter <- 5 * 10 ^ 2
cor.params <- c(0.04, 0.04)
sig.params <- c(0.6 ^ 0.5, 0.6 ^ 0.5)
fix.sigma <- 0.4^0.5
# sigma_prop <- matrix(c(0.138, -0.023, -0.023, 0.1), 2) * 2.38 ^ 2 / 2
sigma_prop <- 0.001 * diag(5)
disc_mat <- cbind(discrimination1, discrimination2)
L_a <- lower.tri(disc_mat, diag = TRUE) * 1
T_gp <- diag(m)
# RUN --------------------------------------------------------------------------
Rcpp::sourceCpp("../src/mirt-gibss-sp.cpp")
source("../R/ggplot-mcmc.R")
Rcpp::sourceCpp("../src/ifa-main.cpp")
# set.seed(5)
system.time(
samples <- ifa_gibbs_sp(response, dist, n, q, m, cor.params, sig.params,
Corr[1:2, 1:2], fix.sigma, sigma_prop, L_a, T_gp, 0.234,
iter)
)
## user system elapsed
## 40.405 23.996 16.568
# system.time(
# samples <- spmirt(response = response, nobs = n, nitems = q, nfactors = 2,
# L_rest = L_a, niter = iter)
# )
samples_tib <- as_tibble.spmirt.list(samples, iter/2)
summary(samples_tib)
## # A tibble: 3,634 x 6
## Parameters `2.5%` `10%` `50%` `90%` `97.5%`
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 V1 -0.668 -0.436 0.278 1.10 1.41
## 2 V2 -2.83 -2.39 -1.63 -0.941 -0.632
## 3 V3 -0.621 -0.391 0.259 0.912 1.24
## 4 V4 0.195 0.445 1.09 1.82 2.43
## 5 V5 -1.25 -0.906 -0.245 0.365 0.683
## 6 V6 -0.520 -0.0358 0.542 1.18 1.68
## 7 V7 -0.717 -0.390 0.212 0.778 1.07
## 8 V8 -1.86 -1.35 -0.724 -0.140 0.145
## 9 V9 -2.26 -1.68 -0.882 -0.196 0.0795
## 10 V10 -1.08 -0.697 0.0152 0.595 0.958
## # ... with 3,624 more rows
samples_long <- gather(samples_tib)
as_tibble.spmirt.list(samples, 0, 10, "c") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, 10, "a") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, iter/2, 10, "a") %>%
gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.0967
as_tibble.spmirt.list(samples, iter/2, 10, "theta") %>%
dplyr::select(1:100) %>%
gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.218
as_tibble.spmirt.list(samples, 0, 10, "theta") %>%
select(1:10) %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, 10, "mgp_sd") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, 10, "mgp_phi") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, 10, "a") %>%
gg_density2d(`Discrimination 1`, `Discrimination 2`, each = 10,
keys = c("Item ", "Discrimination "),
highlight = c(discrimination1, discrimination2))
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
as_tibble.spmirt.list(samples, 0, 10, "a") %>%
gg_scatter(`Discrimination 1`, `Discrimination 2`, each = 10,
keys = c("Item ", "Discrimination "),
highlight = c(discrimination1, discrimination2))
as_tibble.spmirt.list(samples, iter/ 2, select = "a") %>%
summary() %>%
mutate(param = c(discrimination1, discrimination2)) %>%
gg_errorbarh() +
geom_point(aes(param, Parameters), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "c") %>%
summary() %>%
mutate(param = as.numeric(difficulty)) %>%
gg_errorbarh() +
geom_point(aes(param, Parameters), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(1:300) %>%
summary() %>%
mutate(param = data_geo$response[1:300]) %>%
gg_errorbarh(sorted = TRUE) +
geom_point(aes(x = param), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(301:600) %>%
summary() %>%
mutate(param = data_geo$response[301:600]) %>%
gg_errorbarh(sorted = TRUE) +
geom_point(aes(x = param), col = 3)
ability1_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(1:300) %>%
summary() %>%
mutate(param = data_geo$response[1:300],
s1 = data_geo$s1[1:300],
s2 = s1,
estim = `50%`)
ability1_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability1_pred, cutoff = 1, width = 0.01)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 0.7))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 30 rows containing non-finite values (stat_smooth).
## Warning: Removed 30 rows containing missing values (geom_point).
ability2_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(301:600) %>%
summary() %>%
mutate(param = data_geo$response[301:600],
s1 = data_geo$s1[301:600],
s2 = s1,
estim = `50%`)
ability2_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability2_pred, cutoff = 1, width = 0.005)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 0.7))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 60 rows containing non-finite values (stat_smooth).
## Warning: Removed 60 rows containing missing values (geom_point).
# # # PREPARE DATA FOR MODELLING ---------------------------------------------------
# #
# # Y <- data_model %>% dplyr::select(id, response, response_label) %>%
# # spread(response_label, response) %>%
# # arrange(id) %>%
# # dplyr::select(-id) %>%
# # as.matrix()
# #
# # X <- data_model %>% dplyr::select(id, matches("^x[[:digit:]]+$")) %>%
# # unique() %>%
# # arrange(id) %>%
# # dplyr::select(-id) %>%
# # as.matrix()
# #
# # Beta <- matrix(beta, nrow = 1)
# # Sigma_proposal <- diag(1, 3)
# #
# # # RUN MODEL --------------------------------------------------------------------
# #
# # getwd()
# # Rcpp::sourceCpp("../src/multi-lm.cpp")
# # source("../R/ggplot-mcmc.R")
# #
# # iter <- 10^6
# # system.time(
# # samples <- multi_lm(Y, X, iter, 0.01 * Sigma_proposal, 0.001 * Sigma_proposal)
# # )
# # samples %>% map(~ tail(.))
# #
# # # apply(samples$beta, 2, mean)
# # # cor(samples$beta)
# #
# # # Visualize traces
# # as_tibble(samples, 0, 100, select = "beta") %>%
# # gg_trace(wrap = TRUE, alpha = 0.6)
# #
# # as_tibble(samples, 0, 100, select = "beta") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "corr_chol") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "corr") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "sigmas") %>% gg_trace(alpha = 0.6)
# #
# # bla <- as_tibble(samples, iter/2, select = "sigmas")
# # cov(log(bla))
# # nrow(unique(bla)) / nrow(bla)
# #
# # bla <- as_tibble(samples, iter/2, select = "corr_chol")
# # cov(bla)
# # nrow(unique(bla)) / nrow(bla)
# #
# # # Visualize densities
# #
# # as_tibble(samples, iter / 2, select = "corr_chol") %>%
# # gg_density(aes(fill = Parameters), scale = 2, alpha = 0.5, ridges = TRUE)
# #
# # as_tibble(samples, iter / 2, select = "corr") %>%
# # gg_density(aes(fill = Parameters), scale = 1, alpha = 0.5, ridges = TRUE)
# #
# # # Visualize credible intervals
# # as_tibble(samples, iter / 2, select = "beta") %>%
# # summary() %>%
# # mutate(param = beta) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# # Corr_chol <- t(chol(Corr))
# # corr_chol <- Corr_chol[lower.tri(Corr_chol, diag = TRUE)]
# # corr <- Corr[lower.tri(Corr)]
# #
# # as_tibble(samples, iter / 2, select = "corr_chol") %>%
# # summary() %>%
# # mutate(param = corr_chol) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# # as_tibble(samples, iter / 2, select = "corr") %>%
# # summary() %>%
# # mutate(param = corr) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# #
# # as_tibble(samples, iter / 2 ,select = "sigmas") %>%
# # summary() %>%
# # mutate(param = sigmas) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# #
# # # Visualize credible intervals for all Parameters
# # as_tibble(samples, iter / 2) %>%
# # summary() %>%
# # mutate(param = c(beta, corr_chol, corr, sigmas)) %>%
# # gg_errorbar() +
# # geom_point(aes(Parameters, param), col = 3)
# #